A strong law of large numbers for non-additive probabilities

Abstract

In this paper, with the notion of independence for random variables under upper expectations, we derive a strong law of large numbers for non-additive probabilities. This result is a natural extension of the classical Kolmogorov’s strong law of large numbers to the case where the probability is no longer additive. As an application of our result, we give most frequent interpretation for Bernoulli-type experiments with ambiguity.